I need to merge these two objects together, with different geometry
Joining both the mesh will not get a better geometry so i deleted the below part. To get a better geometry.

I added a cube and align little bit near the cut or jaw.

I remove doubles (In edit mode -> select all press W key and remove doubles)

With the helmet selected add boolean modifier -> target the cube and apply

With the below faces selected. Extrude and scale down and once again extrude little.

Add smooth shading

Add edge modifier

Add subsurf modifier

If you see some corner edges.Go to edit mode and select the edges and dissolve them.

This is the result.



Due to large size of gif. click here to watch the preview and to enlarge the preview click on the preview